Chapter 8.5, Problem 3PSA

Solution

To Calculate: The values of p and q .

The values of p and q are $3$ and $22.5$ respectively.

Given information: The measures of other sides i.e., $2,15,6$ and $4$ are provided in the question which will help to find the solution.

Formula used: Here, we are using the concept of Angle Angle similarity.

  

Calculation: Here, In $\Delta ABC$ and $\Delta AED$

  $\angle A=\angle A$ (common)

  $\angle AED=\angle ABC$ (corresponding angles)

  $\therefore \Delta ABC\sim \Delta AED$ (by Angle Angle similarity)

So, $\frac{\text{p}}{\text{2}}\text{=}\frac{\text{6}}{\text{4}}$

➔ $\text{p=3}$

And, $\frac{\text{6}}{\text{2}}\text{=}\frac{\text{q}}{\text{15}}$

➔ $\text{q=}\frac{\text{45}}{\text{2}}\text{=22}\text{.5}$